A256604 Numbers D such that D^2 = A^2 + B^3 + C^4 has more than one solution in positive integers (A, B, C).

5, 9, 12, 17, 19, 21, 23, 25, 28, 33, 35, 37, 38, 39, 42, 45, 46, 47, 51, 53, 55, 57, 59, 60, 61, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 77, 80, 81, 82, 84, 87, 88, 89, 91, 93, 95, 97, 98, 99, 100, 103, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 123, 124, 127, 128, 129, 131, 132, 133, 134, 135, 136, 139, 141

Offset

1,1

Comments

The subsequence of terms of A180241 whose square has more than one representation of the given form. See A256603 and A256652 are the analog for A256091 and A255830.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10088

Example

(A, B, C) = (4, 8, 1): 4^2 + 8^3 + 1^4 = 16 + 512 + 1 = 529 = 23^2 and
(A, B, C) = (1, 8, 2): 1^2 + 8^3 + 2^4 = 1 + 512 + 16 = 529 = 23^2,
so 23 is a term.

Prog

(PARI) for(D=2, 199, my(f=-1, B, D2C4); for(C=1, sqrtint(D), D2C4=D^2-C^4; B=0; while(B++^3<D2C4, issquare(D2C4-B^3)&&f++&print1(D", ")+next(3)))) \\ Converted to integer arithmetic by M. F. Hasler, May 01 2015

Crossrefs

Cf. A180241, A180242, A256613, A255830.

Sequence in context: A314619 A190702 A314620 * A314621 A314622 A314623

Adjacent sequences: A256601 A256602 A256603 * A256605 A256606 A256607

Keyword

nonn

Author

M. F. Hasler, Apr 06 2015

Extensions

Inserted a(7)=23 by Lars Blomberg, Apr 26 2015

Status

approved